406 lines
17 KiB
Lua
406 lines
17 KiB
Lua
---Vector math API documentation
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---Functions for mathematical operations on vectors, matrices and quaternions.
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---
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---
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--- * The vector types (vmath.vector3 and vmath.vector4) supports addition and subtraction
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--- with vectors of the same type. Vectors can be negated and multiplied (scaled) or divided by numbers.
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---
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--- * The quaternion type (vmath.quat) supports multiplication with other quaternions.
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---
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--- * The matrix type (vmath.matrix4) can be multiplied with numbers, other matrices
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--- and vmath.vector4 values.
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---
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--- * All types performs equality comparison by each component value.
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---
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---The following components are available for the various types:
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---
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--- vector3
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---x, y and z. Example: v.y
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--- vector4
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---x, y, z, and w. Example: v.w
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--- quaternion
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---x, y, z, and w. Example: q.w
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--- matrix4
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---m00 to m33 where the first number is the row (starting from 0) and the second
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---number is the column. Columns can be accessed with c0 to c3, returning a vector4.
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---Example: m.m21 which is equal to m.c1.z
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--- vector
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---indexed by number 1 to the vector length. Example: v[3]
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---@class vmath
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vmath = {}
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---Calculates the conjugate of a quaternion. The result is a
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---quaternion with the same magnitudes but with the sign of
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---the imaginary (vector) parts changed:
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---q* = [w, -v]
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---@param q1 quaternion # quaternion of which to calculate the conjugate
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---@return quaternion # the conjugate
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function vmath.conj(q1) end
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---Given two linearly independent vectors P and Q, the cross product,
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---P ? Q, is a vector that is perpendicular to both P and Q and
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---therefore normal to the plane containing them.
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---If the two vectors have the same direction (or have the exact
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---opposite direction from one another, i.e. are not linearly independent)
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---or if either one has zero length, then their cross product is zero.
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---@param v1 vector3 # first vector
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---@param v2 vector3 # second vector
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---@return vector3 # a new vector representing the cross product
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function vmath.cross(v1, v2) end
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---The returned value is a scalar defined as:
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---P ? Q = |P| |Q| cos ?
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---where ? is the angle between the vectors P and Q.
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---
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---
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--- * If the dot product is positive then the angle between the vectors is below 90 degrees.
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---
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--- * If the dot product is zero the vectors are perpendicular (at right-angles to each other).
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---
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--- * If the dot product is negative then the angle between the vectors is more than 90 degrees.
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---@param v1 vector3|vector4 # first vector
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---@param v2 vector3|vector4 # second vector
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---@return number # dot product
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function vmath.dot(v1, v2) end
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---The resulting matrix is the inverse of the supplied matrix.
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--- For ortho-normal matrices, e.g. regular object transformation,
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---use vmath.ortho_inv() instead.
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---The specialized inverse for ortho-normalized matrices is much faster
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---than the general inverse.
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---@param m1 matrix4 # matrix to invert
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---@return matrix4 # inverse of the supplied matrix
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function vmath.inv(m1) end
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---Returns the length of the supplied vector or quaternion.
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---If you are comparing the lengths of vectors or quaternions, you should compare
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---the length squared instead as it is slightly more efficient to calculate
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---(it eliminates a square root calculation).
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---@param v vector3|vector4|quat # value of which to calculate the length
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---@return number # length
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function vmath.length(v) end
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---Returns the squared length of the supplied vector or quaternion.
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---@param v vector3|vector4|quat # value of which to calculate the squared length
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---@return number # squared length
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function vmath.length_sqr(v) end
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---Linearly interpolate between two vectors. The function
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---treats the vectors as positions and interpolates between
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---the positions in a straight line. Lerp is useful to describe
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---transitions from one place to another over time.
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--- The function does not clamp t between 0 and 1.
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---@param t number # interpolation parameter, 0-1
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---@param v1 vector3|vector4 # vector to lerp from
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---@param v2 vector3|vector4 # vector to lerp to
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---@return vector3|vector4 # the lerped vector
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function vmath.lerp(t, v1, v2) end
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---Linearly interpolate between two quaternions. Linear
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---interpolation of rotations are only useful for small
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---rotations. For interpolations of arbitrary rotations,
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---vmath.slerp <> yields much better results.
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--- The function does not clamp t between 0 and 1.
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---@param t number # interpolation parameter, 0-1
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---@param q1 quaternion # quaternion to lerp from
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---@param q2 quaternion # quaternion to lerp to
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---@return quaternion # the lerped quaternion
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function vmath.lerp(t, q1, q2) end
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---Linearly interpolate between two values. Lerp is useful
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---to describe transitions from one value to another over time.
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--- The function does not clamp t between 0 and 1.
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---@param t number # interpolation parameter, 0-1
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---@param n1 number # number to lerp from
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---@param n2 number # number to lerp to
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---@return number # the lerped number
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function vmath.lerp(t, n1, n2) end
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---The resulting identity matrix describes a transform with
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---no translation or rotation.
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---@return matrix4 # identity matrix
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function vmath.matrix4() end
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---Creates a new matrix with all components set to the
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---corresponding values from the supplied matrix. I.e.
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---the function creates a copy of the given matrix.
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---@param m1 matrix4 # existing matrix
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---@return matrix4 # matrix which is a copy of the specified matrix
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function vmath.matrix4(m1) end
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---The resulting matrix describes a rotation around the axis by the specified angle.
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---@param v vector3 # axis
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---@param angle number # angle in radians
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---@return matrix4 # matrix represented by axis and angle
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function vmath.matrix4_axis_angle(v, angle) end
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---The resulting matrix describes the same rotation as the quaternion, but does not have any translation (also like the quaternion).
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---@param q quaternion # quaternion to create matrix from
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---@return matrix4 # matrix represented by quaternion
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function vmath.matrix4_from_quat(q) end
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---Constructs a frustum matrix from the given values. The left, right,
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---top and bottom coordinates of the view cone are expressed as distances
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---from the center of the near clipping plane. The near and far coordinates
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---are expressed as distances from the tip of the view frustum cone.
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---@param left number # coordinate for left clipping plane
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---@param right number # coordinate for right clipping plane
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---@param bottom number # coordinate for bottom clipping plane
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---@param top number # coordinate for top clipping plane
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---@param near number # coordinate for near clipping plane
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---@param far number # coordinate for far clipping plane
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---@return matrix4 # matrix representing the frustum
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function vmath.matrix4_frustum(left, right, bottom, top, near, far) end
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---The resulting matrix is created from the supplied look-at parameters.
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---This is useful for constructing a view matrix for a camera or
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---rendering in general.
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---@param eye vector3 # eye position
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---@param look_at vector3 # look-at position
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---@param up vector3 # up vector
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---@return matrix4 # look-at matrix
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function vmath.matrix4_look_at(eye, look_at, up) end
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---Creates an orthographic projection matrix.
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---This is useful to construct a projection matrix for a camera or rendering in general.
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---@param left number # coordinate for left clipping plane
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---@param right number # coordinate for right clipping plane
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---@param bottom number # coordinate for bottom clipping plane
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---@param top number # coordinate for top clipping plane
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---@param near number # coordinate for near clipping plane
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---@param far number # coordinate for far clipping plane
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---@return matrix4 # orthographic projection matrix
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function vmath.matrix4_orthographic(left, right, bottom, top, near, far) end
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---Creates a perspective projection matrix.
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---This is useful to construct a projection matrix for a camera or rendering in general.
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---@param fov number # angle of the full vertical field of view in radians
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---@param aspect number # aspect ratio
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---@param near number # coordinate for near clipping plane
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---@param far number # coordinate for far clipping plane
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---@return matrix4 # perspective projection matrix
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function vmath.matrix4_perspective(fov, aspect, near, far) end
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---The resulting matrix describes a rotation around the x-axis
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---by the specified angle.
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---@param angle number # angle in radians around x-axis
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---@return matrix4 # matrix from rotation around x-axis
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function vmath.matrix4_rotation_x(angle) end
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---The resulting matrix describes a rotation around the y-axis
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---by the specified angle.
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---@param angle number # angle in radians around y-axis
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---@return matrix4 # matrix from rotation around y-axis
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function vmath.matrix4_rotation_y(angle) end
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---The resulting matrix describes a rotation around the z-axis
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---by the specified angle.
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---@param angle number # angle in radians around z-axis
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---@return matrix4 # matrix from rotation around z-axis
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function vmath.matrix4_rotation_z(angle) end
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---The resulting matrix describes a translation of a point
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---in euclidean space.
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---@param position vector3|vector4 # position vector to create matrix from
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---@return matrix4 # matrix from the supplied position vector
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function vmath.matrix4_translation(position) end
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---Performs an element wise multiplication between two vectors of the same type
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---The returned value is a vector defined as (e.g. for a vector3):
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---v = vmath.mul_per_elem(a, b) = vmath.vector3(a.x * b.x, a.y * b.y, a.z * b.z)
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---@param v1 vector3|vector4 # first vector
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---@param v2 vector3|vector4 # second vector
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---@return vector3|vector4 # multiplied vector
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function vmath.mul_per_elem(v1, v2) end
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---Normalizes a vector, i.e. returns a new vector with the same
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---direction as the input vector, but with length 1.
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--- The length of the vector must be above 0, otherwise a
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---division-by-zero will occur.
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---@param v1 vector3|vector4|quat # vector to normalize
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---@return vector3|vector4|quat # new normalized vector
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function vmath.normalize(v1) end
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---The resulting matrix is the inverse of the supplied matrix.
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---The supplied matrix has to be an ortho-normal matrix, e.g.
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---describe a regular object transformation.
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--- For matrices that are not ortho-normal
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---use the general inverse vmath.inv() instead.
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---@param m1 matrix4 # ortho-normalized matrix to invert
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---@return matrix4 # inverse of the supplied matrix
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function vmath.ortho_inv(m1) end
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---Calculates the extent the projection of the first vector onto the second.
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---The returned value is a scalar p defined as:
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---p = |P| cos ? / |Q|
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---where ? is the angle between the vectors P and Q.
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---@param v1 vector3 # vector to be projected on the second
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---@param v2 vector3 # vector onto which the first will be projected, must not have zero length
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---@return number # the projected extent of the first vector onto the second
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function vmath.project(v1, v2) end
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---Creates a new identity quaternion. The identity
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---quaternion is equal to:
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---vmath.quat(0, 0, 0, 1)
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---@return quaternion # new identity quaternion
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function vmath.quat() end
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---Creates a new quaternion with all components set to the
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---corresponding values from the supplied quaternion. I.e.
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---This function creates a copy of the given quaternion.
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---@param q1 quaternion # existing quaternion
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---@return quaternion # new quaternion
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function vmath.quat(q1) end
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---Creates a new quaternion with the components set
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---according to the supplied parameter values.
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---@param x number # x coordinate
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---@param y number # y coordinate
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---@param z number # z coordinate
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---@param w number # w coordinate
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---@return quaternion # new quaternion
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function vmath.quat(x, y, z, w) end
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---The resulting quaternion describes a rotation of angle
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---radians around the axis described by the unit vector v.
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---@param v vector3 # axis
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---@param angle number # angle
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---@return quaternion # quaternion representing the axis-angle rotation
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function vmath.quat_axis_angle(v, angle) end
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---The resulting quaternion describes the rotation from the
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---identity quaternion (no rotation) to the coordinate system
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---as described by the given x, y and z base unit vectors.
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---@param x vector3 # x base vector
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---@param y vector3 # y base vector
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---@param z vector3 # z base vector
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---@return quaternion # quaternion representing the rotation of the specified base vectors
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function vmath.quat_basis(x, y, z) end
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---The resulting quaternion describes the rotation that,
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---if applied to the first vector, would rotate the first
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---vector to the second. The two vectors must be unit
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---vectors (of length 1).
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--- The result is undefined if the two vectors point in opposite directions
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---@param v1 vector3 # first unit vector, before rotation
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---@param v2 vector3 # second unit vector, after rotation
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---@return quaternion # quaternion representing the rotation from first to second vector
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function vmath.quat_from_to(v1, v2) end
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---The resulting quaternion describes a rotation of angle
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---radians around the x-axis.
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---@param angle number # angle in radians around x-axis
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---@return quaternion # quaternion representing the rotation around the x-axis
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function vmath.quat_rotation_x(angle) end
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---The resulting quaternion describes a rotation of angle
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---radians around the y-axis.
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---@param angle number # angle in radians around y-axis
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---@return quaternion # quaternion representing the rotation around the y-axis
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function vmath.quat_rotation_y(angle) end
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---The resulting quaternion describes a rotation of angle
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---radians around the z-axis.
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---@param angle number # angle in radians around z-axis
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---@return quaternion # quaternion representing the rotation around the z-axis
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function vmath.quat_rotation_z(angle) end
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---Returns a new vector from the supplied vector that is
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---rotated by the rotation described by the supplied
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---quaternion.
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---@param q quaternion # quaternion
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---@param v1 vector3 # vector to rotate
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---@return vector3 # the rotated vector
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function vmath.rotate(q, v1) end
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---Spherically interpolates between two vectors. The difference to
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---lerp is that slerp treats the vectors as directions instead of
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---positions in space.
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---The direction of the returned vector is interpolated by the angle
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---and the magnitude is interpolated between the magnitudes of the
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---from and to vectors.
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--- Slerp is computationally more expensive than lerp.
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---The function does not clamp t between 0 and 1.
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---@param t number # interpolation parameter, 0-1
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---@param v1 vector3|vector4 # vector to slerp from
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---@param v2 vector3|vector4 # vector to slerp to
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---@return vector3|vector4 # the slerped vector
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function vmath.slerp(t, v1, v2) end
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---Slerp travels the torque-minimal path maintaining constant
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---velocity, which means it travels along the straightest path along
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---the rounded surface of a sphere. Slerp is useful for interpolation
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---of rotations.
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---Slerp travels the torque-minimal path, which means it travels
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---along the straightest path the rounded surface of a sphere.
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--- The function does not clamp t between 0 and 1.
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---@param t number # interpolation parameter, 0-1
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---@param q1 quaternion # quaternion to slerp from
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---@param q2 quaternion # quaternion to slerp to
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---@return quaternion # the slerped quaternion
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function vmath.slerp(t, q1, q2) end
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---Creates a vector of arbitrary size. The vector is initialized
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---with numeric values from a table.
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--- The table values are converted to floating point
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---values. If a value cannot be converted, a 0 is stored in that
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---value position in the vector.
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---@param t table # table of numbers
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---@return vector # new vector
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function vmath.vector(t) end
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---Creates a new zero vector with all components set to 0.
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---@return vector3 # new zero vector
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function vmath.vector3() end
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---Creates a new vector with all components set to the
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---supplied scalar value.
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---@param n number # scalar value to splat
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---@return vector3 # new vector
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function vmath.vector3(n) end
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---Creates a new vector with all components set to the
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---corresponding values from the supplied vector. I.e.
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---This function creates a copy of the given vector.
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---@param v1 vector3 # existing vector
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---@return vector3 # new vector
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function vmath.vector3(v1) end
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---Creates a new vector with the components set to the
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---supplied values.
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---@param x number # x coordinate
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---@param y number # y coordinate
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---@param z number # z coordinate
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---@return vector3 # new vector
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function vmath.vector3(x, y, z) end
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---Creates a new zero vector with all components set to 0.
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---@return vector4 # new zero vector
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function vmath.vector4() end
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---Creates a new vector with all components set to the
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---supplied scalar value.
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---@param n number # scalar value to splat
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---@return vector4 # new vector
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function vmath.vector4(n) end
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---Creates a new vector with all components set to the
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---corresponding values from the supplied vector. I.e.
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---This function creates a copy of the given vector.
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---@param v1 vector4 # existing vector
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---@return vector4 # new vector
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function vmath.vector4(v1) end
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---Creates a new vector with the components set to the
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---supplied values.
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---@param x number # x coordinate
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---@param y number # y coordinate
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---@param z number # z coordinate
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---@param w number # w coordinate
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---@return vector4 # new vector
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function vmath.vector4(x, y, z, w) end
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return vmath |